Purely analytic solutions of the compressible boundary layer flow due to a porous rotating disk with heat transfer

Abstract

The motivation of the present study is to obtain exact analytical solution of the steady laminar flow of a compressible viscous fluid over a rotating disk subjected to a uniformly applied suction or blowing. Classical Von Karman problem of a rotating disk is extended to account for the compressibility effects with insulated and isothermal wall conditions. Using Von Karman similarity transformation the compressible nonlinear equations of motion are reduced to a boundary value problem whose solution was first obtained by Ackroyd [J. A. D. Ackroyd, “On the steady flow produced by a rotating disc with either surface suction of injection,” J. Eng. Phys. 12, 207 (1978)] for the velocity field in terms of a series of exponentially decaying functions. This kind of an approach, however, besides being incapable of resolving the velocity field for higher values of injection (see the conclusion of Ackroyd) is also shown not to be suitable for the temperature distribution of the compressible flow, necessitating the use of a Chebyshev collocation technique in such circumstances. A universally valid analytical technique based on the homotopy analysis method is next applied to obtain solutions corresponding to both velocity and temperature fields. This method yields explicit analytic solutions converging uniformly to the exact solution having the form of exponentially decaying functions for the full range of parameters considered. The effects of suction and blowing together with compressibility on the physically relevant and significant parameters are rigorously explored from the exact formulas extracted.